"It was one simple mistake. It was just a slip, an unintentional error. We were not trying to bend the rules."
The family's application to stay in the UK indefinitely was refused because they missed the deadline.
"We are utterly distraught at the thought of our lives being devastated because of a technicality. This is our home. I would serve a prison sentence to sort this out."
Talbot, a teacher, who runs cheese-making classes for the Women's Institute and Waitrose, described the decision to reject the application as "criminal".
The family had been visiting Dorset for more than 30 years when they decided to move there permanently in 2010. They qualified for ancestry visas because Talbot's grandmother was born in the UK.
They knew their visas would expire in May last year and intended to apply for indefinite leave to remain as soon as possible - 28 days before they would expire. But that required them to pass a Life in the UK test as part of their application.
Talbot and husband John, 62, passed first time but Charles, 21, was studying for exams at the Royal Agricultural University and did not pass until after the deadline had expired. Edward, 24, was born in the UK and so has dual citizenship.
When the family produced their finished application - at a cost of £5700 ($10,340) - they were told it was unsuccessful because they had missed the 28-day window.
Their passports were seized and they were told they could not appeal. They have now been told to "leave the UK voluntarily" or they will be "liable for enforced removal".
But an immigration judge has urged the Home Office to take a "benevolent view" following a hearing of the case in February.
Justice Jay said: "There is really no reason, frankly, why this application should be refused if the applicants can meet what I would like to call the substantive requirements, namely the fact of ancestry and the fact that they now successfully have all passed this test."
The family are now calling on British Immigration Minister Robert Goodwill to intervene and save them from deportation.
Edward, whose plan for a dairy and beef farm has been on hold for a year now, said: "It is an extreme case of bureaucracy gone mad.
"We need the immigration minister to understand this case is absolute nonsense and use the power available to him to grant the application.
"We came here legally, we haven't submitted false documents, and we haven't committed any crimes. In any other walk of life or business it just wouldn't happen."
The case has echoes of the problems facing the Brain family, who settled in the Scottish Highlands on a student visa - but the terms of their stay were later changed by the Government and they are fighting deportation.
Robert Talbot has links to Dorset dating back 42 years when he went over from New Zealand to work on a farm for a year. He and his wife have been married 32 years and regularly returned to the county before deciding to settle.
They now say their farm cottage near Blandford Forum feels like their true home.
The family GP, writing a reference for the family, said they were "honest, hard-working and reliable", and the stress of the "unfair" situation had caused them health problems.
The Home Office did not respond to requests for comment.
